Question:
I am flying to Beziers and was wondering if you are aware of services (bus or train to Bize-Minervois).

Answer:
As far as I can tell there is no bus service between Beziers and Bize-Minervois. I’m also not sure about train. Bize-Minervois might not have a train station. It looks to be about a 35 minute drive so maybe you might look into car hire. This B&B has a nice getting here page.